Author's Accepted Manuscript

Author's Accepted Manuscript
Author’s Accepted Manuscript


Evaluating ‘‘Cash-for-Clunkers’’: Program Effects
on Auto Sales and the Environment
Shanjun Li, Joshua Linn, Elisheba Spiller




                                                                         www.elsevier.com/locate/jeem

PII:               S0095-0696(12)00067-8
DOI:               http://dx.doi.org/10.1016/j.jeem.2012.07.004
Reference:         YJEEM1746

To appear in:      Journal of Environmental Economics and Management

Received date:     3 October 2011
Revised date:      9 July 2012
Accepted date:     13 July 2012

Cite this article as: Shanjun Li, Joshua Linn and Elisheba Spiller, Evaluating ‘‘Cash-for-
Clunkers’’: Program Effects on Auto Sales and the Environment, Journal of
Environmental         Economics       and     Management,       http://dx.doi.org/10.1016/
j.jeem.2012.07.004

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to the journal pertain.
Evaluating “Cash-for-Clunkers”: Program Effects on

                          Auto Sales and the Environment1
                           Shanjun Li, Joshua Linn, and Elisheba Spiller


                                              Abstract
         “Cash-for-Clunkers” was a $3 billion program that attempted to stimulate the
         U.S. economy and improve the environment by encouraging consumers to
         retire older vehicles and purchase fuel-efficient new vehicles. We investigate
         the effects of this program on new vehicle sales and the environment. Using
         Canada as the control group in a difference-in-differences framework, we find
         that, of the 0.68 million transactions that occurred under the program, the
         program increased new vehicle sales only by about 0.37 million during July
         and August of 2009, implying that approximately 45 percent of the spending
         went to consumers who would have purchased a new vehicle anyway. Our
         results cannot reject the hypothesis that there is little or no gain in sales
         beyond 2009. The program will reduce CO2 emissions by only 9 to 28.2
         million tons based on upper and lower bounds of the estimate of the program
         effect on sales, implying a cost per ton ranging from $92 to $288 even after
         accounting for reduced criteria pollutants.


Keywords: Stimulus, Cash-for-Clunkers, Auto Demand, CO2 emissions
JEL Classifications: Q50, H23, L62


1
   Shanjun Li is an Assistant Professor in the Dyson School of Applied Economics and Management at
Cornell University, 424 Warren Hall, Ithaca, NY, 14853, email: sl2248@cornell.edu, phone: (607)255-
1832, fax: (607)255-9984. Joshua Linn is a Fellow at Resources for the Future (RFF), 1616 P Street NW,
Washington, DC, 20036, email: linn@rff.org, phone: (202)328-5047, fax: (202)939-3460. Elisheba
Spiller is a Post-Doctoral Research Fellow at RFF, email spiller@rff.org, phone: (202)328-5147, fax:
(202)939-3460. We thank Soren Anderson, Antonio Bento, Maureen Cropper, Robert Hammond, Paul
Portney, Kevin Roth, and Chris Timmins for helpful comments and Jeffrey Ferris, Marissa Meir and Shun
Chonabayashi for excellent research assistance. This paper supersedes RFF Discussion paper 10-39 titled
Evaluating “Cash for Clunkers”: Program Effects on Auto Sales, Jobs and the Environment.

                                                  1

1. Introduction

Amid a major recession and growing concerns about the environment, many countries have
adopted programs that encourage consumers to trade in their old, inefficient vehicles in exchange
for more efficient ones. In the United States, the Cash-for-Clunkers program provided eligible
consumers a $3,500 or $4,500 rebate when trading in an old vehicle and purchasing or leasing a
new vehicle. Many other countries, such as France, the United Kingdom, and Germany, have
similar programs, which generally share the same goals: to provide stimulus to the economy by
increasing auto sales, and to improve the environment. The U.S. program received enormous
media attention and many considered the program to be a great success; during the program’s
nearly one-month run, it generated 678,359 eligible transactions and had a cost of $2.85 billion.2
But as a matter of economic theory, it is typically quite difficult to achieve multiple goals with a
single policy. The large fiscal cost and public enthusiasm for these programs, and their
widespread use around the world, raise the question of just how effective they are at meeting
their economic and environmental goals.

        This study estimates the composition of the fleet of vehicles that would have been sold in
the absence of the program, permitting a comprehensive evaluation of the program effect on
vehicle sales, the environment and economic activity. First, we examine the program effects on
the quantity and composition of new vehicle sales both during the program and in the several
months before and after the program. Many observers of the program were concerned that it
would primarily pull demand from adjacent months, thus providing little short-term stimulus,
while others believed that the program would pull demand from several years in the future
(Council of Economic Advisors, 2009). Furthermore, we are interested in analyzing whether the
program affected the fuel economy distribution of new vehicle sales. Because Cash for Clunkers
was promoted for stimulus and environmental reasons, we focus on two types of changes in
consumer behavior caused by the program: switching from purchasing low fuel-efficiency to



2
   Transportation Secretary LaHood declared the program to be “wildly successful” at the end of the
program, while two Op-Ed articles in the Wall Street Journal on August 2nd and 3rd raised doubts about
whether the program truly increased sales and stimulated the economy. They argued that the program
would most likely result in the shifting of future vehicle demand to the present and could hurt the sales of
other goods.

                                                     2

high fuel-efficiency vehicles, and shifting the purchase time to take advantage of the program’s
incentives.

       Second, we evaluate the program’s cost-effectiveness in reducing gasoline consumption
and carbon dioxide (CO2) emissions by comparing total gasoline consumption as well as
emissions of CO2 and criteria pollutants with and without the program. There exist many federal
subsidy programs aiming to reduce U.S. gasoline consumption and CO2 emissions such as tax
credits for ethanol blending and income tax incentives for purchasing hybrid vehicles. Our cost-
effectiveness analysis permits a comparison across these different programs.

       The basis for these evaluations is the difference-in-differences (DID) analysis in a vehicle
demand framework based on monthly sales of new vehicles by model from 2007 to 2009. The
U.S. market constitutes the treatment group in the analysis. We use Canada as the control group
based on two observations as well as some statistical evidence. First, Canada did not have a
similar program, while nearly a dozen European countries did in 2008 and 2009. Second, the
Canadian auto market is probably the most similar to the U.S. market: in both countries in recent
years before the recession, about 13-14 percent of households annually purchased a new vehicle;
characteristics of vehicles sold are similar; and pre-program time trends are similar. The two
main identifying assumptions are that the program did not affect the Canadian vehicle market
and that the differential effect of the 2008-2009 recession across the two countries’ vehicle
markets did not vary over the months in 2009. We provide some evidence supporting these
assumptions in Section 3.3.

       The DID analysis shows that the program increased sales of vehicles that were eligible
for the rebate (eligible vehicles) and lowered sales of ineligible vehicles during the program
period. Furthermore, within eligible vehicles, the positive effect was larger for those with higher
fuel efficiency – which yield a higher rebate under the program. The negative effect on ineligible
vehicles was stronger for those that barely missed the eligibility requirement, implying that the
program caused consumers to substitute from these vehicles to eligible vehicles. We find that the
program reduced sales in the months before and especially after the program, and that the effect
on sales weakened over time. The empirical results thus suggest that the program shifted
consumer demand from ineligible vehicles to eligible ones as well as from pre- and post-program
periods to program periods, with the inter-temporal shift having the strongest impact.

                                                3

With the parameter estimates from the DID analysis, we simulate vehicle sales in the
counterfactual scenario of no program. We find that the program increased sales by only 0.37
million during July and August of 2009, implying that of the 0.66 million vehicles in our sample
that were purchased under the program, 0.29 million would have been purchased anyway during
these two months. The program effect on vehicle sales erodes further when we look at a longer
time horizon: the increase in vehicle sales during June to December of 2009 was practically zero.
In addition, our simulation results show that Toyota, Honda and Nissan benefited from the
program disproportionally more than other firms: with a combined market share of around 38
percent before the program, they accounted for more than 50 percent of the increased sales. The
U.S.-based automakers and their dealers were facing especially low revenues prior to the
program, and although sales of the vehicles produced by these automakers increased by about 14
percent in July and August, over the June-December period sales increased by less than one
percent. Therefore, we conclude that the program provided little economic stimulus beyond late
2009.

        Based on the simulation results for vehicle sales, we estimate the differences in total
gasoline consumption, CO2 emissions, and four criteria pollutant emissions (carbon monoxide,
volatile organic compounds, nitrogen oxides and exhaust particulates) with and without the
program. We provide the results for 12 different cases, across which parameter and behavior
assumptions vary. Over the vehicles’ lifetimes, the reduction in gasoline consumption ranges
from 924.5 to 2,907.3 million gallons while that in CO2 emissions ranges from 9 to 28.2 million
tons. By comparison, in 2009, U.S. gasoline consumption was 141 billion gallons and CO2
emissions from passenger vehicles were 1.1 billion metric tons. After accounting for the
program’s benefit in reducing criteria pollutants, we estimate that the program’s cost of CO2
emissions reduction ranged from $92 to $288 per ton of CO2 while that of gasoline consumption
reduction ranged from $0.89 to $2.80 per gallon.

        Several recent studies have evaluated particular aspects of the Cash-for-Clunkers
program. Knittel (2009) estimates the implied cost of the program in reducing CO2 emissions.
Council of Economic Advisors (CEA 2009) and Cooper et al. (2010) analyze program impacts
on vehicle sales and employment. National Highway and Traffic Safety Administration (NHTSA,
2009) also examines program effects on gasoline consumption and the environment. The major


                                               4

difference between our analysis and the aforementioned studies lies in the fact that we use the
DID approach to estimate counterfactual sales by vehicle model in the absence of the program.
Knittel (2009) does not establish the counterfactual and does not examine program effects on
vehicle sales. The other three studies estimate the sales effect based on heuristic rules and
aggregate sales data and do not examine consumer substitution across models and over time.

       A recent study by Mian and Sufi (2010) is more closely related to ours in that we both
establish counterfactual outcomes by exploiting variations in program exposure across different
areas. Rather than using Canada as a control group, that paper uses the number of “clunkers”
registered in U.S. cities prior to the program as a measure of ex-ante program exposure.
Variation in this measure identifies the program effect, and the paper shows an almost identical
short-term effect (July and August) to ours. They argue that by as early as March 2011, the
program effect was completely reversed. Copeland and Kahn (2011) use a time-series approach
to examine the program effect on sales and on production. They find a slightly larger short-term
effect on vehicles sales but they also conclude that by January 2010, the cumulative effect of the
program on sales was essentially zero. Neither of these papers examines environmental outcomes.

       Carefully analyzing the counterfactual is important for estimating the environmental
benefits of the program. For example, we find a smaller cost per ton of CO2 reduction than
Knittel (2009) because we account for the difference between total CO2 emissions during the
remaining lifetime of the trade-in vehicles and the emissions from the new vehicles purchased to
replace them, and the fact that the fleet of new vehicles purchased under the program is more
fuel efficient than that without the program; Knittel (2009) only considers the first effect. Failing
to analyze the counterfactual fleet without the program can thus underestimate the program’s
environmental benefit.


2. Background and Data

In this section, we first discuss the background of the Cash-for-Clunkers program, including the
timeline and eligibility rules. Next, we present the data that are used in the empirical analysis.


2.1 Program Description


                                                  5

As Figure 1 shows, the Consumer Assistance to Recycle and Save (CARS) Act was passed by
the House of Representatives on June 9th, 2009 and by the Senate on June 18th, and was signed
into law by the President on June 24th. The law established the Cash-for-Clunkers program, a
temporary program granting subsidies to individuals who trade in their older, fuel inefficient,
vehicle to purchase a new and more efficient vehicle. The traded-in vehicle would then be
dismantled in order to ensure that it does not return to the road. The program was officially
launched on July 27th, 2009 and terminated ahead of schedule on August 25th, 2009. It generated
678,359 eligible transactions at a cost of $2.85 billion.3 Originally, the program was planned as a
$1 billion program with an end date of November 1st, 2009.

                        Figure 1: Timeline of the Cash-for-Clunkers Program
     June 9           June 24            July 27                          August 25
    “C-f-C”           President          CARS program                     CARS program
     approved         signed CARS        officially launched              ended
     by House                            by NHTSA

       June 18                July 24                                           November 1
       Bill approved          Final rules                                       Projected
       by Senate              issued                                            end date


                                                                                    
                                                                                   
               Pre-Program Period                Program Period                     Post- Program Period


        The Cash-for-Clunkers program was intended to reduce the number of old and less fuel
efficient vehicles (i.e. clunkers) on the roads as well as shift demand towards more fuel efficient
new vehicles. The program outlined four requirements that the trade-in would have to meet in
order to be eligible, as shown in Table 1A. These requirements varied according to the size and
class of the vehicle. The first three requirements ensured that the traded-in vehicle would
otherwise be on the road had it not been for the program: the trade-in vehicle must be drivable; it
must have been continually insured and registered by the same owner for the past year; and it
must be less than 25 years old. The fourth rule ensured that the vehicle is in fact a “clunker”: it




3
   Statistics are from press releases at http://www.cars.gov/official-information.

                                                       6

must have a combined fuel efficiency of 18 mpg or less (the latter two requirements were
different for category 3 trucks).4

       Table 1B shows the minimum MPG a new vehicle needed to qualify. The MPG
requirement was 22 for passenger automobiles, 18 for category 1 trucks, and 15 for category 2
trucks. Category 3 trucks, on the other hand, had no minimum fuel efficiency requirement, but
they could only be traded in for category 3 trucks. Finally, the manufacturer’s suggested retail
price (MSRP) of the new vehicle could not exceed $45,000. Table 1B shows that the stringency
of the MPG requirement was greatest for passenger cars and decreased across the truck
categories. For example, a new passenger car must have an MPG improvement of at least 4 over
the trade-in vehicle in order to qualify for the $3,500 rebate while a 10 MPG improvement is
needed for the $4,500 rebate. For a new vehicle in category 1, the requirements on the MPG
improvement are 2 and 5 for the two rebate levels. The requirements become even less stringent
for category 2 and 3 vehicles.


2.2 Data Description

We collect data on monthly vehicle sales for all models in the United States and Canada from
2007 to 2009 from Automotive News. We combine these data with vehicle MPG data from the
Environmental Protection Agency’s fuel economy database as well as vehicle prices and other
characteristics from Wards’ Automotive Yearbook. Our data include 16,776 observations of
monthly vehicle sales. We define a model as a country-vintage-nameplate (e.g., a 2007 Toyota
Camry in the United States) and we have 1,436 models in the data. Almost all models sold in
Canada are available in the United States.

       Table 2 provides summary statistics of the data set. Based on the eligibility rules, 1,008
of the 1,436 vehicle models meet the requirement and could be eligible for the rebate during the
program (henceforth, eligible vehicles). Among the 16,776 observations, about 70 percent of
sales in both countries are for eligible vehicles. As shown in the table, the eligible vehicles have
much higher sales than ineligible ones. Although average sales per model in the United States are

4
   Category 1 trucks are “non-passenger automobiles” including SUVs, medium-duty passenger vehicles,
pickup trucks, minivans and cargo vans. Category 2 trucks are large vans or large pickup trucks whose
wheelbase exceeds 115 inches for pickups and 124 for vans. Category 3 trucks include very large pickup
trucks and cargo vans.

                                                   7

much higher than in Canada, the number of new vehicles sold per household is 13-14 percent in
both countries. On average, the eligible vehicles are cheaper and, by definition, more fuel-
efficient than the ineligible ones. The average prices (sales-weighted) are very similar in the two
countries across both categories. Because the share of light trucks in total sales is larger in
Canada than the United States, the average fuel efficiency of vehicles in Canada in both
categories is lower than in the United States.

       To examine the effectiveness of the program on energy consumption and the environment,
we use the public database for the Cash-for-Clunkers program from www.cars.gov. The data set
provides (dealer-reported) information on the trade-in and new vehicles for each transaction
during the program. There are 678,539 transactions in the data set. We remove transactions that
are subject to reporting error (e.g., reported MPG that does not meet the eligibility criteria). In
addition, we delete 2,278 category 3 vehicles and 6,169 leased vehicles in order to be consistent
with our demand analysis of new vehicles. After removing 18,959 records, there are 659,400
observations of trade-in and new vehicles under the program.

       Table 3 shows the summary statistics on trade-in and new vehicles. This table
demonstrates that consumers were trading in more light trucks than cars, and that these trucks
were newer than the cars. Our final sample has an average rebate amount of $4,214 and a total
payment of $2.78 billion (out of $2.85 billion for all transactions in the full data set).


3. Empirical Strategy

In this section, we first discuss the channels through which the program could affect vehicle sales.
We then describe our empirical model.


3.1 Potential Program Effects

In our analysis, we assume that the program did not affect vehicles sales prior to June 2009.
Although some consumers may have known about the bill before the House passed it on June 9th,
we expect that the uncertainty surrounding the eligibility requirements as well as the bill’s final
passage would greatly limit its effect before June 9th. In fact, our estimation results show that
there is no significant effect on sales even in June. The program period is defined from July 27th

                                                   8

to August 25th. Although the program retrospectively recognized qualified sales from July 1st
until the official start date, the total number of these pre-program sales was only 30,317, which is
less than the average daily sales during the first week of the program.

       Because an automobile is a durable good, the program could affect vehicle sales before,
during, or after the program period. During the program period, some consumers who would
have purchased an ineligible model or chosen not to purchase a new vehicle may choose to
purchase an eligible model instead, as depicted in Figure 2. In addition, the program could result
in consumers changing the purchase time in order to coincide with the program period (i.e.,
intertemporal substitution). In the absence of the program, these consumers could have
purchased an eligible or an ineligible vehicle in other periods. Both channels would increase
total vehicle sales and likely improve fleet fuel-efficiency. To a large extent, the design of the
program in achieving the stimulus purpose was to pull demand forward from a sufficiently distant
future when the economy was expected to be stronger. Thus, the time horizon over which the
intertemporal substitution occurs is crucially important to the stimulus purpose but not so for the
environmental purpose. The graph below illustrates the different substitution channels.

                             Figure 2: Diagram of Program Effects
        Choices \ Timing           Pre-program           Program          Post-program
                                   06/01-07/26         07/27-08/25            08/26-

        Ineligible Vehicle


        Eligible Vehicle


        No Purchase



       The degree of these substitutions could vary over product space as well as over time for
several reasons. First, there could be a stronger substitution to eligible vehicles from vehicles that
barely miss the MPG requirement, compared to the substitution from vehicles that have much
lower fuel efficiency. This is due to the fact that higher fuel-efficiency vehicles tend to


                                                  9

compromise on certain amenities such as horsepower and engine size, and thus a consumer
would face a smaller trade off in amenities by only marginally increasing fuel efficiency. In
addition, because high MPG vehicles could be eligible for a higher rebate ($4,500 versus $3,500)
the program could have a stronger effect on the vehicles eligible for the higher rebate. Second,
the substitution could exhibit heterogeneity over time. Intuitively, the intertemporal substitution
should be stronger right before or after the program than farther away from the program.
Moreover, because the length of the program is not fixed and runs out when the designated
amount of stimulus money is used up, the program could have a stronger stimulus effect at the
beginning of the program period. In fact, the initial one billion dollars were used up within a
week while the additional two billion dollars lasted for three weeks. Thus, we explicitly model
and measure these substitution patterns in our estimation.


3.2 Empirical Model

We implement the DID method in a regression framework where the Canadian auto market is
used as the control group for the U.S. market. Our DID regression estimates how the program
affected vehicle sales before, during, and after the program period on a monthly basis given the
vehicle’s eligibility and other characteristics. The causal interpretation hinges on the identifying
assumption that (unobserved) demand and supply shocks at the time of the program are the same
across the two countries. Section 3.3 presents analysis suggesting that Canada is a valid control
group to estimate underlying trends that are not affected by the program but that do affect vehicle
sales (such as economic shocks that occur at the same time as the program).

       The regression model is based on monthly sales of new vehicles by vehicle model. Let c
index country (United States or Canada), t index year, m index month, and j index vehicle
nameplate (e.g., Ford Focus). We define a vehicle model as a country-year-nameplate (e.g., a
2009 Ford Focus in the United States) and use ctj as the index. By including interactions of
month dummies with eligibility in a regression framework, the program can have different
effects across months and eligibility status. This allows us to identify both the intertemporal and
cross-model substitution patterns discussed in the previous section.




                                                10

We define Ectj as the eligibility dummy, equal to one for any vehicle in either country that meets
the program requirement (irrespective of whether the program is in effect) and zero otherwise.
  I ctj is a dummy variable for ineligible vehicles and is equal to one for any vehicle in either
country that does not meet the program requirement. Pctm is a dummy variable equal to one for
months when the program may have had an effect (e.g., June to December of 2009) in the United
States and zero otherwise. The interaction of the program dummy with eligibility dummies
indicates models that are in the program and are eligible for the rebate. Equation (1) allows us to
disentangle monthly program effect on sales for eligible and ineligible vehicles.



                                        log qctmj       Ectj PctmD tmE  I ctj PctmD tmI

 xctmj D  [ctj  EctjKcm
                        E
                            I ctjKcm
                                   I
                                       EctjG tmE  I ctjG tmI  H ctmj , (1)

where qctmj is the sales of vehicle model j.5 The first term on the right side captures the program
effect on eligible vehicles during the relevant months while the second term captures that on
ineligible vehicles. Instead of estimating the program effects for pre-program, during-program,
and post-program periods, we estimate the effects month by month using this flexible
specification for two reasons: (1) the program period does not coincide with a full month and our
data are at the monthly level; and (2) the nature of intertemporal substitution would imply a
diminishing impact farther away from (either before or after) the program period.

          The first two terms capture the program effect on vehicle sales in the United States and
these two terms are zero for the observations in Canada. However, interpreting these coefficients
as causal program effects hinges on the assumption that Canada is a valid control group. The
other variables in the equation help identify the impact of the program on sales by controlling for
observed and unobserved country and vehicle attributes.
Because the program affected demand for eligible vehicles in proportion to their fuel efficiency,
we must control for the effect on sales of fuel costs, which also depends on fuel efficiency.


5
   For all the regressions presented in the paper, we also estimate a multinomial logit model in the linear
form (Berry 1994) where we assume that consumers have a total of J vehicle models plus an outside good
indexed by 0 (i.e., not purchasing a new vehicle) to choose from in a given month. The dependent
variable is log( S ctmj )  log( S ctm 0 ) with S ctmj and Sctm 0 being the market shares of model j and the
outside good that captures the decision of not purchasing a new vehicle. The market size is the number of
households in the two countries. The results are very close to the results from the linear models shown in
Section 4.


                                                              11

Variables in xctmj include dollars per mile (gasoline price/MPG), which is proportional to the
lifetime fuel costs of the vehicle assuming the price of gasoline follows a random walk. Several
recent empirical studies have documented a negative relationship between fuel costs and vehicle
sales (e.g., Busse et al. 2009, Li et al. 2009, and Klier and Linn 2010). We allow the coefficient
on dollars per mile to be different in these two countries. Since we control for model (country-
year-nameplate) fixed effects, vehicle MPG itself is subsumed in these fixed effects.

    [ ctj denotes model (i.e., country-year-nameplate) fixed effects, which control for month-
invariant observed and unobserved vehicle attributes (such as horsepower, weight, and product
quality), as well as month-invariant demand shocks at the model level. K cm
                                                                         E
                                                                            and K cm
                                                                                  I
                                                                                     are country-
month fixed effects to capture country-specific seasonality for eligible and ineligible vehicles
(such as the December holiday effect). [ctj ,Kcm
                                              E
                                                 , and K cm
                                                         I
                                                            are all country-specific fixed effects,
controlling for country-specific demand and supply shocks that affect the level of vehicle sales
(these would be equivalent to household or firm dummies in a canonical DID example). Because
the fixed effects vary by nameplate-year-country, we allow for the possibility that the recession
or other shocks affected the U.S. and Canadian vehicle markets differently each year. G tmE and
G tmI are year-month fixed effects for eligible and ineligible vehicles (these would be equivalent to
time dummies in a canonical DID example) common across countries. Because these fixed
effects are used to capture demand shocks for the two groups of vehicles that are common in the
two automobile markets, they give rise to the control group interpretation for the Canadian
market.6 Finally, H ctmj is the random demand shock.

          Although equation (1) provides a starting point for our analysis, it does not allow
heterogeneous program effects across vehicles within the same eligibility category.
Heterogeneous effects could exist among both eligible and ineligible vehicles for the reasons
noted in the previous section. First, since there are two rebate levels ($3,500 and $4,500) and the
size of the rebate depends on the difference between the MPG of the new vehicle and that of the
trade-in vehicle, consumers may substitute towards eligible vehicles with higher MPGs as these
vehicles are more likely to provide them with a $4,500 rebate. Second, the program effect on
ineligible vehicles could be correlated with fuel efficiency as well: consumers are more likely to
switch from barely ineligible vehicles to eligible vehicles, rather than substitute away from
vehicles much farther from the eligibility cut-off. Due to the trade-offs between vehicle
size/horsepower and fuel efficiency, consumers likely suffer a smaller sacrifice in vehicle size or
horsepower by switching from barely ineligible vehicles to eligible ones, rather than from

6
   Because not all models are available in both countries, we cannot use year-month-model fixed effects.

                                                    12

vehicles that are far below the MPG requirements. To capture the heterogeneous effect, we
estimate equation (2) as our main specification.
                             log qctmj       Ectj PctmD tmE  Ectj Pctm GPM ctj E tmE

                                     I ctj PctmD tmI  I ctj Pctm | GPM ctj | EtmI

               xctmj D  [ctj  EctjKcm
                                      E
                                          I ctjKcm
                                                 I
                                                     EctjG tmE  I ctjG tmI  H ctmj . (2)

GPM is gallons per mile and CGPM j                1/ MPG j  1/ MPG* , where MPG * is the MPG
requirement for rebate eligibility, which varies across vehicle categories as discussed in Section
2.1. Thus, GPM ctj measures how far a vehicle’s fuel efficiency is from the eligibility
requirement. The farther away a vehicle’s fuel efficiency is from the requirement (for either an
eligible or ineligible vehicle), the larger the variable is. The second and fourth terms on the right
side of the equation capture the heterogeneous program effect for vehicles within the same
eligibility category. As the results show below, although equations (1) and (2) provide similar
estimation results for the program effect on vehicle sales, equation (2) leads to a much larger
effect on average vehicle fuel economy (and hence a larger environmental benefit and energy
savings).


3.3 Canada as the Control Group

In this section, we provide qualitative and quantitative support for using Canada as the control
group. First, Canada did not have a similar program, whereas many European countries including
Germany, France, Italy and Spain did in 2008 and 2009. Although Canada has a Retire Your
Ride Program that started in January 2009, the program is not comparable to the Cash-for-
Clunkers program for at least three reasons. First, the program provides only CA$300 worth of
credit for eligible participants (owners of pre-1996 model-year vehicles that are in running
condition), compared to $3,500 or $4,500 offered in the United States. Second, the goal of the
Canadian program is to improve air quality by encouraging people to use environmental-friendly
transportation, so the program is not tied to new vehicle purchases. Depending on the province,
the credit can be a public transit pass, a membership to a car-sharing program, cash, or a rebate
on the purchase of a 2004 or newer vehicle. Third, the program only retired about 60,000
vehicles during the first 15 months. Therefore, its effect on new vehicle sales (about 1.6 million
annually) should be negligible.


                                                           13

The second justification for using the Canadian auto market as the control group is that it
is probably the most similar to the U.S. market. About 13-14 percent of households purchased a
new vehicle in recent years before the economic downturn in both countries. Table 2 also shows
that the vehicles sold have similar characteristics, although the U.S. market has a larger set of
models. Figure 3 depicts monthly sales in logarithm of all, eligible, and ineligible new vehicles
in the two countries from 2007 to 2009. By and large, the two series track each other well. A
noticeable difference is that sales in Canada seem to have stronger seasonality (e.g., a larger
hump during March-May each year), suggesting the importance of controlling for country-
specific seasonality in our analysis.

Our empirical models given in equations (1) and (2) control for unobservables in several
dimensions by including model fixed effects [ ctj , common year-month fixed effects G tm , and
country-specific seasonality Kcm . Nevertheless, as we discussed above, the unbiasedness of the
coefficient estimates hinges on the identifying assumption that the time trends in demand and
supply are the same in the two countries. Otherwise, we risk interpreting preexisting differences
in time trends as the effect of the program.

        The economic downturn that started in the second half of 2008 raises a particular concern
that the demand and supply trends were not similar in the two markets. The recession in the
United States was driven by the housing market crisis; the mortgage default rate increased
dramatically and housing prices fell sharply at the onset of the crisis. By comparison, housing
prices in Canada continued to increase until late 2008. In addition, the credit market in Canada
was not impaired and did not experience the same “credit crunch” as the United States. As a
result, the downturn in Canada was milder and the auto market in Canada did not contract as
much as in the United States. 7,8

        It is important to note that because equation (2) includes nameplate-country-year fixed
effects, our model allows for the possibility that the recession differentially affected the U.S. and
Canadian markets. For example, the estimated program effects would not be biased if the auto


7
   We examine the trends of durable goods sales across both countries during this time and find similar
pre-trend declines in spending across electronics, appliances, and new vehicles.
8
   Although GDP growth, employment, and household spending slowed in Canada, the decrease in total
new vehicle sales in the second half of 2008 was less severe in Canada: sales dropped 1.1% in Canada in
2008 (against a 1.5% increase in 2007) while they dropped 18% in the United States (against a 3% drop in
2007).

                                                  14

market contracted in 2008 to different degrees in the U.S. and Canada. Nevertheless, we must
maintain the assumption that the differences across countries in the effects of the recession do
not vary over the year, which raises two concerns. First, we control for seasonality by including
country-month fixed effects, but the estimated fixed effects would be biased if, for example, the
downturn in August 2008 was more severe than in other months in 2008; in turn this would bias
the estimated program effects. To address this concern, we drop the data from June to December
of 2008 as an alternative to the estimation using the full data set. If the downturn were causing
significant bias, we would expect to obtain different results by omitting these observations. As
we show below, we obtain qualitatively similar results from these two estimations. The second
concern about the recession is that the effects of the recession immediately before, during, or
after the program may have been different than the effects at other times during 2009. In the
difference-in-difference framework, we maintain the identifying assumption that the relative
effects of the recession on the United States and Canada were similar throughout 2009. If the
recession had a larger negative effect on the U.S. market during the months prior to the program
than during the program, the estimated program effects would be biased away from zero.
This identifying assumption cannot be directly tested, but we can take advantage of the data
before the program period to examine differences in pre-existing trends. Similarity before the
program would support the assumption that the trends are the same during and afterwards. To
that end, we estimate equation (2) without the first four terms on the right hand side using data
before June 2009 (i.e., before the program affected the market). Figure 4 plots the aggregate
monthly sales after removing the effects from observed variables ( xctmj ) , time trends G tm , and
seasonality Kcm . The three panels show that underlying vehicles sales (i.e., residuals) track each
other quite well in the two countries before the program.

       To gauge the importance of using the Canadian market as the control group, we estimate
a model without the control group and present the results in the online appendix (Appendix
Tables 2 and 3) posted at the journal’s online repository of supplemental material, which can be
accessed via www.aere.org/journals). We find much larger program effects on vehicle sales from
this analysis than the DID analysis in both the short and long run. In addition, we do not find that
the positive sales effect erodes over time, suggesting a lack of evidence of intertemporal
substitution. This demonstrates the importance of having a valid control group; ignoring the
underlying trend biases the results and causes the program to look much more successful than it
truly was. Thus, in the main text, we focus on the DID analysis as our main specification.

                                                 15

4. Estimation Results

We first present parameter estimates for equations (1) and (2). We then discuss program effects
on vehicle sales and fuel economy implied by these parameter estimates.



4.1 Difference-in-Differences Results

Table 4 reports parameter estimates and standard errors for three regressions. The first regression
is equation (1) while the second one is equation (2), both using the full sample. The third
estimation is for equation (2) based on the sample without the second half of 2008 (shorter
sample). We only report the coefficient estimates associated with program effects (June to
December of 2009) for the two groups of vehicles, noting that the full set of control variables
described after equation (1) is included in the regressions; estimates of the other coefficients
have the expected signs and are available upon request.9 In the second and third regressions, we
include the interaction of the vehicle eligible dummy and |GPM| to allow for heterogeneous
effects across vehicles.10 For example, in the top panel, the first row shows the effect of the
program on sales of eligible vehicles in June, i.e., before the program begins. The second row
shows whether the effect is larger for vehicles that are further from the MPG requirement.
Subsequent rows show analogous coefficients for other months, and the bottom panel reports
coefficient estimates for ineligible vehicles. Throughout the paper, standard errors are
constructed using block bootstrap and are robust to heteroskedasticity and serial correlation
within a vehicle model (country-year-nameplate). We also estimate standard errors with two
alternative block definitions: country-nameplate and nameplate. The standard errors are slightly
smaller under both alternative definitions. As a conservative measure, we present the standard
errors using a vehicle model as a block in the main text. The alternative standard errors for the
simulations of program effects are presented in the online appendix (Appendix Table 4).

        Overall, the parameter estimates have the expected signs. The directions of the program
effect on sales suggested by the parameter estimates are similar across all three estimations, and

9
 For the second regression, the coefficient estimates on dollars per mile are -9.877 (1.249) for Canada,
and -10.075 (1.254) for the United States. The estimates are negative as well in the other two regressions.
10
    The mean of |GPM| for eligible vehicles in 2009 in the United States is 0.67 with a range from 0 to
2.61. The mean of |GPM| for ineligible vehicles is 0.67 with a range from 0.21 to 1.70.

                                                    16

we focus on the full-sample results. The fourth column in the top panel in Table 4 shows the
parameter estimates using the full sample. The two coefficient estimates for June suggest that the
program reduced sales of eligible vehicles but the reduction is smaller for high MPG vehicles,
both without statistical significance. The two coefficient estimates for July capture the combined
effects from the pre-program period (July 1st-26th) and the program period (27th-31st). We would
expect a decrease in sales during the pre-program period and an increase during the program
period. Therefore, the combined effect could be positive or negative. The coefficient estimates
using the full sample suggests that the program reduced the sales of eligible vehicles with low
MPG while it increased the sales of those with high MPG. Similarly, the coefficients for August
capture the combined effect during the program (August 1st-25th) and post-program (August 26th-
31th). The coefficient estimates imply that the combined effect on eligible vehicles was positive
and that the increase in sales was larger for eligible vehicles with high MPG. These results imply
that the positive program effect outweighed the negative intertemporal substitution effect in both
July and August.

        The coefficient estimates for September suggest that the program reduced sales of
eligible vehicles and that the decrease in sales was larger for eligible vehicles with high MPGs,
consistent with consumers moving purchases forward to take advantage of the program. The
parameter estimates for October and November suggest a negative effect on sales but the
estimates are not statistically significant.

        For ineligible vehicles, the parameter estimates suggest a negative effect from July to
December and a larger effect for vehicles that miss the MPG requirement by a smaller margin
(e.g., a smaller |GPM|). This is consistent with the fact that when consumers switch from these
vehicles to eligible vehicles, they do not need to make a large sacrifice in other vehicle attributes
such as horsepower and size, as discussed in Section 3. The third column shows that the results
are qualitatively similar for the short sample, both for eligible and ineligible vehicles.

        It is important to point out that our empirical model assumes that there are no interactions
between the two markets (e.g., the Cash-for-Clunkers program does not affect the Canadian
market). Sales may be correlated across countries for a variety of reasons, but a particular
concern for the empirical strategy would be if demand in the U.S. affects the availability or
prices of vehicles in Canada. For example, during the program the greater U.S. demand for


                                                  17

eligible vehicles could cause manufacturers to divert to the U.S. market eligible vehicles that
would otherwise have been supplied to Canada.11 This would decrease sales of eligible vehicles
in Canada, and potentially bias the estimated program effects away from zero. In that sense we
consider the reported estimates to be an upper bound, which strengthens the main conclusion that
the program had a very small effect on total sales.12


4.2 Program Effect on New Vehicle Sales and Fuel Efficiency

Based on the parameter estimates from Table 4, we simulate new vehicle sales under the
counterfactual scenario without the Cash-for-Clunkers program. The two plots in Figure 5 show
sales effects for eligible and ineligible vehicles from June to December of 2009 for the full
sample based on parameter estimates from equation (2). Dashed curves represent the 90 percent
confidence intervals estimated by bootstrap. The point estimates show the differences between
observed and simulated sales. The corresponding plots in Figure 6 are based on parameter
estimates using the short pre-program sample.

        The results in both figures demonstrate the two channels through which the program
affects vehicles sales (as discussed in Section 3.1). First, the sales of eligible vehicles increased
in July and August but decreased in adjacent months, implying that some consumers shifted their
purchase timing. Second, the program had a strong positive effect for eligible vehicles in August
but a negative effect for ineligible vehicles from July to December, especially in August,
suggesting that some consumers switched from ineligible vehicles to eligible vehicles.

        The effect on sales in June was negative but not statistically different from zero in both
estimations, supporting our modeling assumption that the program effect before June was
negligible. Because the program was implemented from July 27th-August 25th, the effect on total
sales in July and August captures the (positive) effect during the program period and the
(negative) effect due to intertemporal substitution just before or after the program. The net
effects are both positive in July and August, although the effect in July is not statistically

11
    The abrupt start of the program, the short program-period, and the large vehicle inventories before the
program started make this less likely to have occurred.
12
    Another interaction between the two countries can occur if manufacturers made strategic pricing
decisions across both countries, thus the boom in demand due to the program in the United States could
potentially affect supply in Canada. However, the short timing of the program and the relatively small
amount of extra vehicles sold during the period most likely mitigates this effect.

                                                     18

significant in the second estimation. The sales effects are all negative in September to November
from both figures, particularly in the second estimation.

        Figure 7 shows the cumulative effects over different time horizons. The left-most point
shows the cumulative effect during July-August. The points to the right show that the positive
effects eroded over time. The top plot (based on the full sample) shows that the net effect is not
statistically different from zero by the end of October. The bottom plot (based on the short pre-
program sample) shows the same result by the end of September. Both plots show that the
program likely had a short-lived effect on total vehicle sales.

        Panel 1 of Table 5 reports monthly observed and simulated sales of new vehicles from
June to December of 2009. Column (1) gives the observed sales while columns (2) and (3)
provide the estimated sales effects and standard errors based on the parameter estimates from
equation (1) using the full sample. Columns (4) to (5) provide results based on the parameter
estimates from equation (2) using the full sample. Columns (6) and (7) are results using the short
pre-program sample.

        The estimated sales effects are similar across all three regressions. The cumulative effect
on sales during July and August is estimated to range from 345,000 units to 405,000.
Specification two provides an estimate of 370,000, in the middle of the range. This suggests that
out of the 660,000 program participants, about 290,000 would have purchased a new vehicle
during July and August even without the program. This underscores that one cannot take the
number of vehicles sold through the program as the net program effect on vehicle sales. In
addition, the estimate suggests that about 45 percent of the total spending ($1.4 billion) went to
consumers who would have purchased a new vehicle anyway. Looking at a longer horizon,
neither of the estimates suggests a net gain in sales during the period from June to December.
Our estimate of the short-term effect on sales of about 360,000 is essentially identical to that of
Main and Sufi (2010), despite the fact that different control groups are used. The point estimate
is smaller than the 450,000 units from Copeland and Kahn (2011), but their estimate is within the
90 percent confidence interval of ours. In addition, all three studies broadly conclude that the
program effect on sales is short-lived, with ours suggesting an even shorter effect.13


13
    Copeland and Kahn (2011) argue that Canada had a milder downturn than the United States and as a
result the rebound in the second half of 2009 could be milder as well. If our model was not able to address

                                                    19

The second and third panels in Table 5 show the program effect on the average MPG and
GPM (gallons per 100 miles) of the new vehicles for two time horizons: July-August, and June-
December. Although the three regressions provide similar estimates of the program’s effect on
sales, the regression based on equation (1) yields a smaller estimate of the program’s effect on
vehicle fuel efficiency. During July and August, the program increased the average MPG of new
vehicles by 0.65 (from 22.72 to 23.37) based on the second regression, compared to only 0.23
based on the first regression. This highlights the importance of allowing heterogeneous effects as
in equation (2) in evaluating the program impact. Over a longer time horizon, the effect on
average MPG diminished: although the program increased sales of high MPG vehicles in July
and August, it actually reduced sales of those vehicles in other months. Although our results
suggest that the net effect of the program on vehicle sales was likely zero by the end of 2009, the
program did increase the average MPG of new vehicles purchased.

              Table 6 reports the sales effects for individual firms during July-August, and June-
December of 2009. Toyota experienced the biggest increase in sales while Chrysler experienced
the smallest in both time horizons based on the results from the full sample. Although accounting
for less than 40 percent of the market share, the three Japanese firms accounted for over 50
percent of the sales increase because they offer more fuel-efficient models than the U.S.-based
firms. Although the results for the period of June-December provide evidence that the program
did not lead to significant shifts in market shares among automakers, the (relatively small)
increase in sales could have provided important, although short-lived, support to cash-stricken
GM and Chrysler (Hortaçsu et al. 2011).


5. Program Effects on Gasoline Consumption and the Environment

This section evaluates the effectiveness of the program in reducing gasoline consumption and
CO2 emissions. To that end, we compare the observed outcomes (i.e., gasoline consumption and
CO2 emissions) with the counterfactual outcomes in the absence of the program. In this section,
we first discuss our method and then present the results.



this, we should have under-estimated the negative effect on vehicle sales from September to December of
2009.

                                                                                             20

5.1 Method

The program affected gasoline consumption and pollution through two channels. First, the
program changed the fleet of new vehicles by causing some consumers to switch from fuel-
inefficient vehicles to fuel-efficient vehicles, and by causing other consumers to purchase a new
vehicle when they would not have otherwise. Second, it affected the fleet of used vehicles
because the trade-in vehicles were scrapped. A complete analysis of the two channels would
involve an equilibrium model of the auto market (including both new and used vehicles) that
includes the dynamic effects of the program on both channels in a unifying framework.

       Instead, we investigate the two channels based on the results from the previous section
together with some simplifying assumptions. The first assumption is that the scrappage of the
trade-in vehicles did not affect the remaining fleet of used vehicles. To the extent that the
program reduced the availability of used vehicles in the second-hand market and hence increased
used vehicle prices and prolonged their service, our analysis would over-estimate the energy and
environmental benefits of the program.

       The second assumption concerns the long-term program effect on vehicle sales. Because
of the difficulty in obtaining precise estimates of the sales effect during June to December, we
estimate the environmental and energy impacts based on two alternative scenarios. Our results
based on both samples cannot reject a zero net effect during June to December of 2009. That is,
total sales of new vehicles under the counterfactual would be the same as the observed total sales.
We maintain this assumption in the first scenario, which we report in the main text.

       In an alternative scenario, which we report in the online appendix 3, we allow for the
possibility that the program increased June-December sales. In constructing this scenario, we
note that the 90% upper bound for the sales effect in June to December is 834,337 units, while
that for July-August is 566,145. Because of intertemporal substitution the program effect is
unlikely to be larger for longer time horizons; therefore, we use 566,145 as the estimate for the
June-December effect in the alternate scenario.

       To estimate the environmental and energy impacts, we compare gasoline consumption in
the actual (with the policy) and counterfactual (without the policy) scenarios. This difference can




                                                  21

be represented by the difference between the objects in (3) and (4). Equation (3) is the actual
gasoline consumption over the lifetime of the vehicles sold from June to December of 2009:

GAS     ¦( q
         j
               j   *VMT j * GPM j ),                                 (3)


where q j is the total sales of vehicles of model j during the period, and VMT j is the lifetime
vehicle miles traveled for model j. Lu (2006) estimates that the average lifetime VMT for
passenger cars is 152,137 and that for light trucks is 179,954 based on the 2001 National
Household Travel Survey. GPM j is fuel consumption, which is measured in gallons per mile.

        Under the two assumptions discussed above, there are two components of counterfactual
gasoline consumption: (1) the amount consumed over their remaining lifetime by the clunkers
that were not traded in; and (2) the amount consumed by the new vehicles that would have been
purchased from June to December of 2009 (with the time horizon to be discussed further below):
        K                             
GAS     ¦RVMTk * GPM k  ¦ q j *VMT j * GPM j ,
        k 1                       j
                                                                           (4)


where RVMTk is the remaining VMT of the trade-in vehicle k. We estimate the remaining VMT
of each of the trade-in vehicles based on Lu (2006)’s estimates of age-specific survival
probabilities and estimated annual VMT for passenger cars and light trucks as shown in
Appendix Table 1 in the online appendix. With this information, we predict age-specific
remaining VMT for each type of vehicle, which is also shown in that table. Based on this
method, the average remaining VMT of trade-in vehicles is 59,716 with an average remaining
lifetime of 7 years.14 The second term in equation (4) is the total lifetime gasoline consumption
                                                                                   
of new vehicles sold from June to December in the absence of the program. q j is the simulated
                                                                                       
sales of model j based on estimation results in the previous section. We adjust q j proportionally
so that total sales of new vehicles are the same under the two scenarios. This analysis amounts to
the assumption that consumers as a whole would have kept their trade-in vehicles for their
remaining lifetime and in addition purchased the same number of new vehicles during June to
December as in the with-policy scenario. The total effect of the policy during the 7-month period


14
    We compared the trade-in vehicles to the vehicles from the 2001 National Household Survey (NHTS),
which is a national survey on vehicle holdings and travel behavior. On average, the trade-in vehicles have
higher mileage than the vehicles with the same age from the 2001 NHTS. The difference is larger for
relatively new vehicles. Therefore, our analysis could overestimate the remaining lifetime of the trade-in
vehicles and the environmental benefit of the program. Nevertheless, the majority of the trade-in vehicles
are 10-20 years old and the average MPG of these vehicles are quite close in these two data sets.

                                                   22

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